Inaccuracies in carrier-phase estimation and amplitude equalization cause distortions, i.e., the noise enhancements, which reduce the performance of optical communications systems. In the optical communications, different algorithms are used to reduce the distortion. Those algorithms are based on a hard decision for determining the phase and amplitude of the received signal. For example, a decision-directed least-mean-square (LMS) method uses the hard decision for determining the error for the updating.
However, the hard decisions can be incorrect causing suboptimal phase and amplitude equalization. The problem of inaccuracy of the hard decisions is especially apparent in the applications with low signal-to-noise ratios (SNR). However, for each fixed SNR, there is a need to further improve the data throughput and other performance metrics of optical communications, such as spectral efficiency of the transmitted signal.
In order to provide higher optical interface rates, recent research has focused on the expansion of both bandwidth and spectral efficiency. While some researches have focused on the slicing of the received signals in the time or frequency domains, these solutions require several parallel coherent receivers. Current results using a single coherent receiver have exceeded 640 Gb/s net bit rate. However, there is a demand to provide a system and a method for detection of a net bit rate in excess of 1 Tb/s with a single coherent receiver.
Detection of the bit rates in excess of 1 Tb/s with a single receiver requires accurate demodulation of the signals. To demodulate signals in an optical communications system, it is necessary to equalize distortions to both phase and amplitude of the received signals, caused by the optical and electrical components. This is particularly difficult for densely modulated signals with high-order quadrature-amplitude modulation (QAM), such as 64-QAM and 256-QAM.
Some conventional systems, such as a system described in U.S. Pat. No. 8,320,778, perform amplitude equalization using a radius-directed constant-modulus algorithm (CMA) equalizer, with an updating algorithm, such as an LMS method. That method yields acceptable results with high SNR and reasonably low density modulation, e.g., 8QAM, 16QAM. However, densely modulated signals that can result in bit rates in excess of 1 Tb/s can cause significant tap noise at the equalizer output, due to the inaccuracy of the blind decisions based on the radius of the received signals.
For equalization of phase distortions, conventional systems can use a blind phase search approach, see, e.g., U.S. 2011/0217043. However, that approach has a high complexity for densely modulated signals and suffers from poor performance in a low SNR regime.